By bus
Albuquerque has a fine bus depot at the Alvarado Transportation Center in downtown, 320 First St SW, which is served by Greyhound +1 505 243-4435, (http://www.greyhound.com) and Autobuses Americanos (http://www.autobusesameri...) which provides bus service to many points in Mexico. The depot has a small cafeteria.
By plane
Albuquerque's airport, the Albuquerque International Sunport IATA: ABQ (http://www.cabq.gov/airport/), is the major air hub for all of New Mexico. American, Continental, Delta, Frontier, United, and US Airways serve the Sunport with limited service to their respective major hubs, but it's Southwest Airlines that operates most traffic into ABQ, with direct service to most western cities as well as some of Southwest's hubs in the Midwest and eastern United States. There is also commuter service to destinations within New Mexico provided by Great Lakes and New Mexico Airlines.
One tip: If you're prone to airsickness, try to get flights into this airport that arrive either before noon or after sundown, particularly during late spring and early summer. The high elevation, hot sun, and spring winds combine to produce thermals that can make afternoon arrivals an extremely bumpy proposition. There are no major safety issues the airport's runways are long, owing to the adjacent Air Force base, with no nearby obstacles to run into, but try telling your stomach that! The rough ride is less of a problem with outbound flights.
Incidentally, this airport contains a number of attractive displays of New Mexican arts and crafts, and is a more pleasant place than most airports to kill time while waiting for a flight. The Sunport also has charging stations for electronics and free wireless internet access. The major car rental companies are nearby, with a shuttle from the airport to the large rental center. The airport is served by a number of shuttle services as well as local bus #50, located on the lower level at the west end of the shuttle island (http://www.cabq.gov/airpo...).
By train
Albuquerque is a layover stop along Amtrak's Southwest Chief (http://www.amtrak.com/ser...) daily train route. The depot is at the Alvarado Transportation Center in downtown, at 320 First St SW in the same building as the Greyhound depot. The westbound train to Los Angeles is scheduled to arrive at 3:55PM and departs at 4:45PM. The eastbound train to Chicago arrives at 12:12PM and departs at 12:55PM. The station has a small cafeteria.
A commuter rail line, the New Mexico Rail Runner Express (http://www.nmrailrunner.com), connects Albuquerque to Santa Fe and to the smaller communities north and south along the Rio Grande, including Belen, Los Lunas, and Bernalillo. There are three stations: the Alvarado Transportation Center in Downtown, one in the South Valley on Rio Bravo Blvd, and one in the North Valley/Los Ranchos area just off of Paseo del Norte. The Downtown station has bus connections to the airport. The Rail Runner runs daily, although service can be limited outside the weekday rush hour periods. Fares are based on how far you ride; a day pass will usually be in the range of $5-9. Tickets can be purchased online (http://www.nmrailrunner.c...) or from ticket agents on the train.
By car
Two interstate highways pass through: I-40 goes east-west and I-25 goes north-south. Where they meet is a large intersection called "The Big I". Albuquerque's Central Ave. is part of old Route 66. A minor note of caution: I-25 south of the city is a "safety corridor" in which state law mandates higher fines for traffic violations. Enforcement is spotty, but take the speed limits seriously anyway.